Question

The size of each interior angle of a regular polygon is 156 degrees. Work out the number of sides the polygon has.

Answer 1

$\alpha = \frac{n-2}{n} \cdot 180 \ \ \ \ \ \ \ [\alpha =interior\ angle, \ n=number \ of \ sides] \\ \\ 156=\frac{n-2}{n} \cdot 180 \\ 156n=(n-2)180 \\ 156n = 180n - 360 \\ 360 = 180n-156n \\ 360 = 24n \\ n=360/24=15$

The polygon has 15 sides.